The odd-order nonzero domination-root conjecture for generalized friendship graphs

Let $F_{4,n}$ be the generalized friendship graph with parameter $n$, and let a domination root mean a real zero of its domination polynomial $D(F_{4,n},x)$. Odd-order nonzero-root conjecture. For every odd natural number $n$, no nonzero real number is a domination root of $F_{4,n}$. This is presented as a conjectural root property of the domination polynomial; the supplied source does not establish its status.